From Invariant

Walking a group

Without retracing your steps, which walks bring you back to the start?

Your walke

Drag to turn the shape.

Three Cayley graphs from Chapter IV of Invariant. Each point is an element of the group, each colour of line a generator. A walk that comes back to the start without retracing its steps is a rule of the group. Each kind of face is one of the basic rules; a larger loop encloses several faces, and its rule follows from theirs.